Discussiones Mathematicae Differential Inclusions 19 (1999) 45-65

[BIBTex]

ON THE SOLUTION SET OF THE NONCONVEX SWEEPING PROCESS

Andrea Gavioli

Dipartimento di Matematica Pura e Applicata
Universita di Modena, via Campi 213/B, 41100 Modena, Italy

e-mail: gavioli@unimo.it

Abstract

We prove that the solutions of a sweeping process make up an Rδ-set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.

Keywords: nonconvex, sweeping process, wedged.

1991 Mathematics Subject Classification: 34A60, 34C25.

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Received 5 June 1999